Compressed Sensing for Multidimensional Spectroscopy Experiments

Fisher information for smart sampling in time-domain spectroscopy

Time-domain spectroscopy encompasses a wide range of techniques, such as Fourier-transform infrared, pump-probe, Fourier-transform Raman, and two-dimensional electronic spectroscopies. These methods enable various applications, such as molecule characterization, excited state dynamics studies, or spectral classification. Typically, these techniques rarely use sampling schemes that exploit the prior knowledge scientists typically have before the actual experiment. Indeed, not all sampling coordinates carry the same amount of information, and a careful selection of the sampling points may notably affect the resulting performance. In this work, we rationalize, with examples, the various advantages of using an optimal sampling scheme tailored to the specific experimental characteristics and/or expected results. We show that using a sampling scheme optimizing the Fisher information minimizes the variance of the desired parameters. This can greatly improve, for example, spectral classifications and multidimensional spectroscopy. We demonstrate how smart sampling may reduce the acquisition time of an experiment by one to two orders of magnitude, while still providing a similar level of information.

A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy

Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.

Two-Dimensional Infrared Spectroscopy of Isolated Molecular Ions

Two-dimensional infrared (2D IR) spectroscopy of mass-selected, cryogenically cooled molecular ions is presented. Nonlinear response pathways, encoded in the time-domain photodissociation action response of weakly bound N2 messenger tags, were isolated using pulse shaping techniques following excitation with four collinear ultrafast IR pulses. 2D IR spectra of Re(CO)3(CH3CN)3+ ions capture off-diagonal cross-peak bleach signals between the asymmetric and symmetric carbonyl stretching transitions. These cross peaks display intensity variations as a function of pump-probe delay time due to coherent coupling between the vibrational modes. Well-resolved 2D IR features in the congested fingerprint region of protonated caffeine (C8H10N4O2H+) are also reported. Importantly, intense cross-peak signals were observed at 3 ps waiting time, indicating that tag-loss dynamics are not competing with the measured nonlinear signals. These demonstrations pave the way for more precise studies of molecular interactions and dynamics that are not easily obtainable with current condensed-phase methodologies.

Ultrafast transient vibrational action spectroscopy of cryogenically cooled ions

Ultrafast transient vibrational action spectra of cryogenically cooled Re(CO)3(CH3CN)3+ ions are presented. Nonlinear spectra were collected in the time domain by monitoring the photodissociation of a weakly bound N2 messenger tag as a function of delay times and phases between a set of three infrared pulses. Frequency-resolved spectra in the carbonyl stretch region show relatively strong bleaching signals that oscillate at the difference frequency between the two observed vibrational features as a function of the pump-probe waiting time. This observation is consistent with the presence of nonlinear pathways resulting from underlying cross-peak signals between the coupled symmetric-asymmetric C≡O stretch pair. The successful demonstration of frequency-resolved ultrafast transient vibrational action spectroscopy of dilute molecular ion ensembles provides an exciting, new framework for the study of molecular dynamics in isolated, complex molecular ion systems.

High-sensitivity fluorescence-detected multidimensional electronic spectroscopy through continuous pump-probe delay scan

Fluorescence-detected multidimensional electronic spectroscopy (fMES) promises high sensitivity compared to conventional approaches and is an emerging spectroscopic approach toward combining the advantages of MES with the spatial resolution of a microscope. Here, we present a visible white light continuum-based fMES spectrometer and systematically explore the sensitivity enhancement expected from fluorescence detection. As a demonstration of sensitivity, we report room temperature two-dimensional coherence maps of vibrational quantum coherences in a laser dye at optical densities of ∼2-3 orders of magnitude lower than conventional approaches. This high sensitivity is enabled by a combination of biased sampling along the optical coherence time axes and a rapid scan of the pump-probe waiting time T at each sample. A combination of this approach with acousto-optic phase modulation and phase-sensitive lock-in detection enables measurements of room temperature vibrational wavepackets even at the lowest ODs. Alternative faster data collection schemes, which are enabled by the flexibility of choosing a non-uniform undersampled grid in the continuous T scanning approach, are also demonstrated.

High-resolution two-dimensional electronic spectroscopy reveals the homogeneous line profile of chromophores solvated in nanoclusters

Doped clusters in the gas phase provide nanoconfined model systems for the study of system-bath interactions. To gain insight into interaction mechanisms between chromophores and their environment, the ensemble inhomogeneity has to be lifted and the homogeneous line profile must be accessed. However, such measurements are very challenging at the low particle densities and low signal levels in cluster beam experiments. Here, we dope cryogenic rare-gas clusters with phthalocyanine molecules and apply action-detected two-dimensional electronic spectroscopy to gain insight into the local molecule-cluster environment for solid and superfluid cluster species. The high-resolution homogeneous linewidth analysis provides a benchmark for the theoretical modelling of binding configurations and shows a promising route for high-resolution molecular two-dimensional spectroscopy.

Understanding the interaction of single chromophores with nanoparticles remains a challenging task in nanoscience. Here the authors provide insight into the interaction between isolated base-free phthalocyanine molecules and He and Ne nanoclusters in the gas phase using high-resolution two-dimensional spectroscopy.

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four S_N2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the sole exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

Compressive dual-comb spectroscopy

Broadband, high resolution, and rapid measurements of dual-comb spectroscopy (DCS) generate a large amount of data stream. We numerically demonstrate significant data compression of DCS spectra by using a compressive sensing technique. Our numerical simulation shows a compression rate of more than 100 with a 3% error in mole fraction estimation of mid-infrared (MIR) DCS of two molecular species in a broadband (~ 30 THz) and high resolution (~ 115 MHz) condition. We also numerically demonstrate a massively parallel MIR DCS spectrum of 10 different molecular species can be reconstructed with a compression rate of 10.5 with a transmittance error of 0.003 from the original spectrum.

Interplay between coherence-time undersampling and scattered light in two-dimensional electronic spectroscopy

Scanning pulse delays in multi-pulse non-linear optical spectroscopy experiments is a major contributor to lengthy data acquisition. Using large steps for the scan can significantly speed up the experiment. However, an improper choice of step length can cause distortions to the resulting spectra, especially if the light scattered on the sample is mixed into the signal. In this work, we identify potential sources of such distortions and suggest appropriate countermeasures to avoid them while maintaining a faster data collection.

Compressed Sensing for Reconstructing Coherent Multidimensional Spectra

We apply two sparse reconstruction techniques, the least absolute shrinkage and selection operator (LASSO) and the sparse exponential mode analysis (SEMA), to two-dimensional (2D) spectroscopy. The algorithms are first tested on model data, showing that both are able to reconstruct the spectra using only a fraction of the data required by the traditional Fourier-based estimator. Through the analysis of the sparsely sampled experimental fluorescence-detected 2D spectra of LH2 complexes, we conclude that both SEMA and LASSO can be used to significantly reduce the required data, still allowing one to reconstruct the multidimensional spectra. Of the two techniques, it is shown that SEMA offers preferable performance, providing more accurate estimation of the spectral line widths and their positions. Furthermore, SEMA allows for off-grid components, enabling the use of a much smaller dictionary than that of the LASSO, thereby improving both the performance and the lowering of the computational complexity for reconstructing coherent multidimensional spectra.

Optimized reconstructions of compressively sampled two-dimensional infrared spectra

Compressive sampling has the potential to dramatically accelerate the pace of data collection in two-dimensional infrared (2D IR) spectroscopy. We have previously introduced the Generic Iteratively Reweighted Annihilating Filter (GIRAF) reconstruction algorithm to solve the reconstruction in 2D IR compressive sampling. Here, we report a thorough assessment of this method and comparison to our earlier efforts using the Total Variation (TV) algorithm. We show that the GIRAF algorithm has some distinct advantages over TV. Although it is no better or worse in terms of ameliorating the impacts of compressive sampling on the measured 2D IR line shape, we find that the nature of those effects is different for GIRAF than they were for TV. In addition to assessing the impacts on the line shape of a single oscillator, we also test the ability of the algorithm to reconstruct spectra that have transitions from more than one oscillator, such as the coupled carbonyl oscillators in rhodium dicarbonyl. Finally, and perhaps most importantly, we show that the GIRAF algorithm has a distinct denoising effect on the signal-to-noise ratio (SNR) of the 2D IR spectra that can increase the SNR by as much as 4× without any additional signal averaging and collecting fewer data points, which should further enhance the acceleration of data collection that can be achieved using compressive sampling and enable even more challenging experimental measurements.

UV Raman chemical imaging using compressed sensing

Different chemical (hyperspectral) imaging techniques have proven to be powerful tools to provide and illustrate insightful data within a broad range of research areas. The present communication includes proof-of-principle results of UV Raman hyperspectral imaging, achieved via compressed sensing measurements using coded apertures (CA) and a reconstruction algorithm. The simple and cheap CA set up, obtained by a 50% overall transmissive random binary mask (chromium on fused silica with 100 μm × 100 μm pixel size) positioned at the entrance plane of an imaging spectrograph, resulted in an overall high throughput for the UV region of interest. The mask was mounted on a translation stage, allowing reproducible switching to different CA, thus making possible for multi frame CA imaging. Results from a scene containing liquid droplets are shown as examples and, as expected, qualitative improvements in resolution and contrast could be observed in both the spatial and spectral domain as the number of CA frames was increased.

Sparsity Facilitates Chemical-Reaction Selection for Engine Simulations

Analysis of large-scale, realistic models incorporating detailed chemistry can be challenging because each simulation is computationally expensive, and a complete analysis may require many simulations. This paper addresses one such problem of this type, chemical-reaction selection in engine simulations. In this computationally challenging case, it is demonstrated how the important concept of sparsity can facilitate chemical-reaction selection, which is the process of finding the most important chemical reactions for modeling a chemical process. It is difficult to perform accurate reaction selection for engine simulations using realistic models of the chemistry, as each simulation takes processor weeks to complete. We developed a procedure to efficiently accomplish this selection process with a relatively small number of simulations using a form of global sensitivity analysis based on sparse regression. The chemical-reaction selection leads to an analysis of the ignition chemistry as it evolves within the compression-ignition engine simulations and allows for the spatial development of the selected chemical reactions to be studied in detail.

Compressed sensing FTIR nano-spectroscopy and nano-imaging

Infrared scattering scanning near-field optical microscopy (IR s-SNOM) provides for spectroscopic imaging with nanometer spatial resolution, yet full spatio-spectral imaging is constrained by long measurement times. Here, we demonstrate the application of compressed sensing algorithms to achieve hyperspectral FTIR-based nano-imaging at an order of magnitude faster imaging speed to achieve the same spectral content compared to conventional approaches. At the example of the spectroscopy of a single vibrational resonance, we discuss the relationship of prior knowledge of sparseness of the employed Fourier base functions and sub-sampling. Compressed sensing nano-FTIR spectroscopy promises both rapid and sensitive chemical nano-imaging which is highly relevant in academic and industrial settings for fundamental and applied nano- and bio-materials research.

Ultrafast Four-Dimensional Coherent Spectroscopy by Projection Reconstruction

Multidimensional coherent spectroscopy provides insights into the vibronic structure and dynamics of complex systems. In general, the higher the dimensionality, the better the spectral discrimination and the more information that may be extracted about the system. A major impediment to widespread implementation of these methods, however, is that the acquisition time generally increases exponentially with dimensionality, prohibiting practical implementation. We demonstrate the use of nonuniform sampling based on the projection-slice theorem and inverse Radon transform within the context of a fifth-order, 4D technique (GAMERS) designed to correlate the vibrational contributions to different electronic states. Projection-reconstruction (PRO GAMERS) greatly reduces the data sampling requirements without sacrificing frequency resolution. The sensitivity of this technique is demonstrated to surpass conventional uniform sampling by orders of magnitude. The incorporation of projection-reconstruction into multidimensional coherent spectroscopy opens up the possibility to study the structure of complex chemical, biological, and physical systems with unprecedented detail.

Fluorescence Excitation Spectroscopy for Phytoplankton Species Classification Using an All-Pairs Method: Characterization of a System with Unexpectedly Low Rank

An all-pairs method is used to analyze phytoplankton fluorescence excitation spectra. An initial set of nine phytoplankton species is analyzed in pairwise fashion to select two optical filter sets, and then the two filter sets are used to explore variations among a total of 31 species in a single-cell fluorescence imaging photometer. Results are presented in terms of pair analyses; we report that 411 of the 465 possible pairings of the larger group of 31 species can be distinguished using the initial nine-species-based selection of optical filters. A bootstrap analysis based on the larger data set shows that the distribution of possible pair separation results based on a randomly selected nine-species initial calibration set is strongly peaked in the 410-415 pair separation range, consistent with our experimental result. Further, the result for filter selection using all 31 species is also 411 pair separations; The set of phytoplankton fluorescence excitation spectra is intuitively high in rank due to the number and variety of pigments that contribute to the spectrum. However, the results in this report are consistent with an effective rank as determined by a variety of heuristic and statistical methods in the range of 2-3. These results are reviewed in consideration of how consistent the filter selections are from model to model for the data presented here. We discuss the common observation that rank is generally found to be relatively low even in many seemingly complex circumstances, so that it may be productive to assume a low rank from the beginning. If a low-rank hypothesis is valid, then relatively few samples are needed to explore an experimental space. Under very restricted circumstances for uniformly distributed samples, the minimum number for an initial analysis might be as low as 8-11 random samples for 1-3 factors.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Revealing true coupling strengths in two-dimensional spectroscopy with sparsity-based signal recovery

Two-dimensional (2D) spectroscopy is used to study the interactions between energy levels in both the field of optics and nuclear magnetic resonance (NMR). Conventionally, the strength of interaction between two levels is inferred from the value of their common off-diagonal peak in the 2D spectrum, which is termed the cross peak. However, stronger diagonal peaks often have long tails that extend into the locations of the cross peaks and alter their values. Here, we introduce a method for retrieving the true interaction strengths by using sparse signal recovery techniques and apply our method in 2D Raman spectroscopy experiments.

Accelerating two-dimensional infrared spectroscopy while preserving lineshapes using GIRAF

We introduce a computationally efficient structured low-rank algorithm for the reconstruction of two-dimensional infrared (2D IR) spectroscopic data from few measurements. The signal is modeled as a combination of exponential lineshapes that are annihilated by appropriately chosen filters. The annihilation relations result in a low-rank constraint on a Toeplitz matrix constructed from signal samples, which is exploited to recover the unknown signal samples. Quantitative and qualitative studies on simulated and experimental data demonstrate that the algorithm outperforms the discrete compressed sensing algorithm, both in uniform and non-uniform sampling settings.

Advances in multi-dimensional coherent spectroscopy of semiconductor nanostructures

Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

Mapping multidimensional electronic structure and ultrafast dynamics with single-element detection and compressive sensing

Compressive sensing allows signals to be efficiently captured by exploiting their inherent sparsity. Here we implement sparse sampling to capture the electronic structure and ultrafast dynamics of molecular systems using phase-resolved 2D coherent spectroscopy. Until now, 2D spectroscopy has been hampered by its reliance on array detectors that operate in limited spectral regions. Combining spatial encoding of the nonlinear optical response and rapid signal modulation allows retrieval of state-resolved correlation maps in a photosynthetic protein and carbocyanine dye. We report complete Hadamard reconstruction of the signals and compression factors as high as 10, in good agreement with array-detected spectra. Single-point array reconstruction by spatial encoding (SPARSE) Spectroscopy reduces acquisition times by about an order of magnitude, with further speed improvements enabled by fast scanning of a digital micromirror device. We envision unprecedented applications for coherent spectroscopy using frequency combs and super-continua in diverse spectral regions.

Accelerated 2D magnetic resonance spectroscopy of single spins using matrix completion

Two dimensional nuclear magnetic resonance (NMR) spectroscopy is one of the major tools for analysing the chemical structure of organic molecules and proteins. Despite its power, this technique requires long measurement times, which, particularly in the recently emerging diamond based single molecule NMR, limits its application to stable samples. Here we demonstrate a method which allows to obtain the spectrum by collecting only a small fraction of the experimental data. Our method is based on matrix completion which can recover the full spectral information from randomly sampled data points. We confirm experimentally the applicability of this technique by performing two dimensional electron spin echo envelope modulation (ESEEM) experiments on a two spin system consisting of a single nitrogen vacancy (NV) centre in diamond coupled to a single (13)C nuclear spin. The signal to noise ratio of the recovered 2D spectrum is compared to the Fourier transform of randomly subsampled data, where we observe a strong suppression of the noise when the matrix completion algorithm is applied. We show that the peaks in the spectrum can be obtained with only 10% of the total number of the data points. We believe that our results reported here can find an application in all types of two dimensional spectroscopy, as long as the measured matrices have a low rank.

Compressed Sensing for the Fast Computation of Matrices: Application to Molecular Vibrations

This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes the computational bottleneck. We apply this new method to an important problem in computational chemistry: the determination of molecular vibrations from electronic structure calculations, where our results show that the overall scaling of the procedure can be improved in some cases. Moreover, our method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations, resulting in a significant 3× speed-up in actual calculations.

Coherent exciton dynamics in supramolecular light-harvesting nanotubes revealed by ultrafast quantum process tomography

Long-lived exciton coherences have been recently observed in photosynthetic complexes via ultrafast spectroscopy, opening exciting possibilities for the study and design of coherent exciton transport. Yet, ambiguity in the spectroscopic signals has led to arguments against interpreting them in terms of exciton dynamics, demanding more stringent tests. We propose a novel strategy, quantum process tomography (QPT), for ultrafast spectroscopy and apply it to reconstruct the evolving quantum state of excitons in double-walled supramolecular light-harvesting nanotubes at room temperature from eight narrowband transient grating experiments. Our analysis reveals the absence of nonsecular processes, unidirectional energy transfer from the outer to the inner wall exciton states, and coherence between those states lasting about 150 fs, indicating weak electronic coupling between the walls. Our work constitutes the first experimental QPT in a "warm" and complex system and provides an elegant scheme to maximize information from ultrafast spectroscopy experiments.

Reproducing Deep Tunneling Splittings, Resonances, and Quantum Frequencies in Vibrational Spectra From a Handful of Direct Ab Initio Semiclassical Trajectories

A time-dependent semiclassical approach for vibrational spectra calculations is shown to describe deep tunneling splittings, resonances, and quantum frequencies in multidimensional multiwell systems, by propagating a very limited number of classical trajectories. The approach is tested on ammonia by evolving eight trajectories on a full-dimensional PES. Quantum effects are reproduced, and results are in good agreement with time-independent quantum calculations. All the features are maintained when ab initio "on-the-fly" dynamics is adopted, thus demonstrating that precomputation of the PES can be avoided. The approach overcomes the typical scaling issues of quantum mechanical techniques without introducing any simplifications nor reductions of dimensionality of the problem. The proposed methodology is promising for further applications to systems of major complexity.

Computation of Two-Dimensional Spectra Assisted by Compressed Sampling

The computation of scientific data can be very time-consuming, even if they are ultimately determined by a small number of parameters. The principle of compressed sampling suggests that for typical data we can achieve a considerable decrease in the computation time by avoiding the need to sample the full data set. We demonstrate the usefulness of this approach at the hand of two-dimensional (2-D) spectra in the context of ultrafast nonlinear spectroscopy of biological systems where numerical calculations are highly challenging due to the considerable computational effort involved in obtaining individual data points.